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A note on the ergodicity of non-linear autoregressive model


  • An, H. Z.
  • Chen, S. G.


We examine the Markov chain Xt = [Phi](Xt - 1) + [var epsilon]tb, where Xt = (xt, ..., xt - p + 1)[tau], B = (1, 0, ..., 0)[tau]. Under some appropriate conditions on [Phi], we show the ergodicity for {Xt} when E[var epsilon]t2 is suitable small, and the geometric ergodicity when Ee[var epsilon]t is suitably small.

Suggested Citation

  • An, H. Z. & Chen, S. G., 1997. "A note on the ergodicity of non-linear autoregressive model," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 365-372, June.
  • Handle: RePEc:eee:stapro:v:34:y:1997:i:4:p:365-372

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    References listed on IDEAS

    1. Bhattacharya, Rabi & Lee, Chanho, 1995. "On geometric ergodicity of nonlinear autoregressive models," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 311-315, March.
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    Cited by:

    1. Mika Meitz & Pentti Saikkonen, 2008. "Stability of nonlinear AR-GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(3), pages 453-475, May.
    2. Felix Chan & Michael McAleer & Marcelo C. Medeiros, 2015. "Structure and asymptotic theory for nonlinear models with GARCH erros," Economia, ANPEC - Associação Nacional dos Centros de Pósgraduação em Economia [Brazilian Association of Graduate Programs in Economics], vol. 16(1), pages 1-21.
    3. Lee, Oesook, 2000. "On probabilistic properties of nonlinear ARMA(p,q) models," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 121-131, January.
    4. Harvill, Jane L. & Ray, Bonnie K., 2006. "Functional coefficient autoregressive models for vector time series," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3547-3566, August.
    5. Lee, O. & Shin, D.W., 2007. "A note on geometric ergodicity of a multiple threshold AR(1) processes on the boundary region with application to integrated m-m processes," Economics Letters, Elsevier, vol. 96(2), pages 226-231, August.
    6. Hwang, S. Y. & Woo, Mi-Ja, 2001. "Threshold ARCH(1) processes: asymptotic inference," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 11-20, May.


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